If a 1 kg object moving at 3 m/s slows down to a halt after moving 8 m, what is the friction coefficient of the surface that the object was moving over?

2 Answers
Mar 13, 2018

mu_k~~0.0573

Explanation:

It's very useful to organize the given information in a table to be able to identify the formulas that would be efficient to use.
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The acceleration is the variable we need to solve for to acquire the net force on the object. The formula, v^2=v_o^2+2ad where v is the final velocity, v_o is the initial velocity, a is the acceleration, and d is the displacement, best allows us to solve for the net acceleration. With the mass (1 kg), we can calculate the net force.

v^2=v_o^2+2ad
a=(v^2-v_o^2)/(2d)
a=(0^2-3^2)/(2*8)
a=-9/16 m/s^2
SigmaF=m*bar a
SigmaF=-9/16 N

The acceleration that slows this object down comes from the frictional force from the surface that the object is sliding on which is defined as F_f=F_n*mu_k. Assuming the object is on a horizontal surface, the F_n=mg or the gravitational force on the object.

( In the following picture, the direction of movement it to the right, the forces interacting on the y-axis, normal force and gravitational force, are of equal magnitude, and the frictional force is opposite to the motion.)

enter image source here
The net force is equal to the frictional force only since the upward normal force cancels out the downward gravitational force therefore, SigmaF=F_f. By substituting F_f with its definition, we get the equation
SigmaF=F_n*mu_k
Where we can then substitute F_n for mg
SigmaF=mg*mu_k
mu_k=(SigmaF)/(mg)
mu_k=(-9/16N)/(-9.81N)~~0.0573

Mar 13, 2018

mu_k = 0.056

Explanation:

Well, the force of friction F_f is defined as the following...

F_f = mu_k N

And the normal is given by...

N = mg

N = (1)(9.81)

N = 9.81N

So now, we need to calculate an acceleration to get the force of friction. We are assuming in this question that F_(drive) = F_f because all the energy that the mass possess is lost to friction.

v^2=u^2-2as

0^2 = 3^2 -2(8)a

0 = 9-16a

a = (-9)/(16)

a= -0.5625 ms^-2

F_f=ma

F_f=(1)abs(-0.5625)

F_f=0.5625N

mu_k = F_f/N

mu_k = 0.5625/9.81

mu_k = 0.057